The noise generated by the ultrathin centrifugal fan in a laptop can significantly impact user comfort. While optimizing the fan itself for noise control is important, addressing noise propagation is also crucial. Due to space limitations inside a laptop, adding an extra component for noise control is nearly impossible. Therefore, modifying the cooling fin outside of the fan outlet for sound insulation can be an effective solution. A sound insulation cooling fin is proposed to provide broad noise insulation while maintaining proper ventilation. Through the introduction of a coupled area change passage, noise at specific frequencies at the passage outlet can be managed to be insulated due to the destructive interference. The effectiveness of the unit's sound insulation is verified through an impedance tube measurement. Moreover, combining different units can create a multi-peak sound insulation effect which is suitable for various noise conditions. To meet the demand of real situations, a reversal design flow combining neural network and nonlinear constrained optimization algorithm is developed. As a result, a sound cooling fin combing 2 sound insulation units featuring 4013 Hz and 6000 Hz is fabricated and the actual insulation performance is measured in an anechoic chamber. The sound transmission loss at the designed frequency range reaches 5 dB, aligning well with the simulation results. The sound insulation cooling fin has the potential to be widely used for noise control in small-scale electronic devices.